This is the second in a sequence of posts scrutinizing computational functionalism (CF). In my last post, I defined a concrete claim that computational functionalists tend to make:

Practical CF: A simulation of a human brain on a classical computer, capturing the dynamics of the brain on some coarse-grained level of abstraction, that can run on a computer small and light enough to fit on the surface of Earth, with the simulation running at the same speed as base reality^[1], would cause the conscious experience of that brain.

I contrasted this with “theoretical CF”, the claim that an arbitrarily high-fidelity simulation of a brain would be conscious. In this post, I’ll scrutinize the practical CF claim.

To evaluate practical CF, I’m going to meet functionalists where they (usually) stand and adopt a materialist position about consciousness. That is to say that I’ll assume all details of a human’s conscious experience are ultimately encoded in the physics of their brain.

The search for a software/hardware separation in the brain

Practical CF requires that there exists some program that can be run on a digital computer that brings about a conscious human experience. This program is the “software of the brain”. The program must simulate some abstraction of the human brain that:

1. Is simple enough that it can be simulated on a classical computer on the surface of the Earth,
2. Is causally closed from lower-level details of the brain, and
3. Encodes all details of the brain’s conscious experience.

Condition (a), simplicity, is required to satisfy the definition of practical CF. This requires an abstraction that excludes the vast majority of the physical degrees of freedom of the brain. Running the numbers^[2], an Earth-bound classical computer can only run simulations at a level of abstraction well above atoms, molecules, and biophysics.

Condition (b), causal closure, is required to satisfy the definition of a simulation (given in the appendix). We require the simulation to correctly predict some future (abstracted) brain state if given a past (abstracted) brain state, with no need for any lower-level details not included in the abstraction. For example, if our abstraction only includes neurons firing, then it must be possible to predict which neurons are firing at $t_1$ given the neuron firings at $t_0$, without any biophysical information like neurotransmitter trajectories.

Condition (c), encoding conscious experience, is required to claim that the execution of the simulation contains enough information to specify the conscious experience it is generating. If one cannot in principle read off the abstracted brain state and determine the nature of the experience,^[3] then we cannot expect the simulation to create an experience of that nature.^[4]

The search for brain software could be considered a search for a “software/hardware distinction” in the brain (c.f. Marr’s levels of analysis). The abstraction which encodes consciousness is the software level, all other physical information that the abstraction throws out is the hardware level.

Does such an abstraction exist? A first candidate abstraction is the neuron doctrine: the idea that the mind is governed purely by patterns of neuron spiking. This abstraction seems simple enough (it could be captured with an artificial neural network of the same size: requiring around ${10}^{20}$ parameters).

But is it causally closed? If there are extra details that causally influence neuron firings (like the state of glial cells, densities of neurotransmitters and the like), we would have to modify the abstraction to include those extra details. Similarly, if the mind is not fully specified by neuron firings, we’d have to include whatever extra details influence the mind. But if we include too many extra details, we lose simplicity. We walk a tightrope.

So the big question is: how many extra details (if any) must mental software include?

There’s still a lot of uncertainty in this question. But all things considered, I think the evidence points towards an absence of such an abstraction that satisfies these three conditions. In other words, there is no software/hardware separation in the brain.

No software/hardware separation in the brain: a priori arguments

Is there an evolutionary incentive for a software/hardware separation?

Should we expect selective pressures to result in a brain that exhibits causally separated software & hardware? To answer this, we need to know what the separation is useful for. Why did we build software/hardware separation into computers?

Computers are designed to run the same programs as other computers with different hardware. You can download whatever operating system you want and run any program you want, without having to modify the programs to account for the details of your specific processor.

There is no adaptive need for this property in brains. There is no requirement for the brain to download and run new software.^[5] Nor did evolution plan ahead to the glorious transhumanist future so we can upload our minds to the cloud. The brain only ever needs to run one program: the human mind. So there is no harm in implementing the mind in a way arbitrarily entangled with the hardware.

Software/hardware separation has an energy cost

Not only is there no adaptive reason for a software/hardware separation, but there is an evolutionary disincentive. Causally separated layers of abstraction are energetically expensive.

Normally with computers, the more specialized hardware is to software, the more energy efficient the system can be. More specialized hardware means there are fewer general-purpose overheads (in the form of e.g. layers of software abstraction).  Neuromorphic computers - with a more intimate relationship between hardware and software - can be 10,000 times more energy efficient than CPUs or GPUs.

Evolution does not separate levels of abstraction

The incremental process of natural selection results in brains with a kind of entangled internal organisation that William Wimsatt calls generative entrenchment. When a new mechanism evolves, it does not evolve as a module cleanly separated from the rest of the brain and body. Instead, it will co-opt whatever pre-existing processes are available, be that on the neural, biological or physical level. This results in a tangled web of processes, each sensitive to the rest.

Imagine a well-trained software developer, Alice. Alice writes clean code. When Alice is asked to add a feature, she writes a new module for that feature, cleanly separated from the rest of the code’s functionality. She can safely modify one module without affecting how another runs.

Now imagine a second developer, Bob. He’s a recent graduate with little formal experience and not much patience. Bob’s first job is to add a new feature to a codebase, but quickly, since the company has promised the release of the new feature tomorrow. Bob makes the smallest possible series of changes to get the new feature running. He throws some lines into a bunch of functions, introducing new contingencies between modules. After many rushed modifications the codebase is entangled with itself. This leads to entanglement between levels of abstraction.

If natural selection was going to build a codebase, would it be more like Alice or Bob? It would be more like Bob. Natural selection does not plan ahead. It doesn’t worry about the maintainability of its code. We can expect natural selection to result in a web of contingencies between different levels of abstraction.^[6]

No software/hardware separation in the brain: empirical evidence

Let’s take the neuron doctrine as a starting point. The neuron doctrine is a suitably simple abstraction that could be practically simulated. It plausibly captures all the aspects of the mind. But the neuroscientific evidence is that neuron spiking is not causally closed, even if you include a bunch of extra detail.

Since the neuron doctrine was first developed over a hundred years ago, a richer picture of neuroscience has emerged in which both the mind and neuron firing have contingencies on many biophysical aspects of the brain. These include precise trajectories of neurotransmitters, densities in tens of thousands of ion channels, temperature fluctuations, glial details, blood flow, the propagation of ATP, homeostatic neuron spiking, and even bacteria and mitochondria. See Cao 2022 and Godfrey-Smith 2016 for more.

Take ATP as an example. Can we safely abstract the dynamics of ATP out of our mental program, by, say, taking the average ATP density and ignoring fluctuations? It’s questionable whether such an abstraction would be causally closed, because of all the ways ATP densities can influence neuron firing and message passing:

ATP also plays a role in intercellular signalling in the brain. Astrocytic calcium waves, which have been shown to modulate neural activity, propagate via ATP. ATP is also degraded in the extracellular space into adenosine, which inhibits neural spiking activity, and seems to be a primary determinant of sleep pressure in mammals. Within neurons, ATP hydrolysis is one of the sources of cyclic AMP, which is involved in numerous signaling pathways within the cell, including those that modulate the effects of several neurotransmitters producing effects on the neuronal response to subsequent stimuli in less than a second. Cyclic AMP is also involved in the regulation of intracellular calcium concentrations from internal stores, which can have immediate and large effects on the efficacy of neurotransmitter release from a pre-synaptic neuron.

(Cao 2022)

From this quote I count four separate ways neuron firing could be sensitive to fluctuations in ATP densities, and one way that conscious experience is sensitive to it. The more ways ATP (and other biophysical contingencies) entangle with neuron firing, the harder it is to imagine averaging out all these factors without losing predictive power on the neural and mental levels.

If we can’t exclude these contingencies, could we include them in our brain simulation? The first problem is that this results in a less simple program. We might now need to simulate fields of ATP densities and the trajectories of trillions of neurotransmitters.

But more importantly, the speed of propagation of ATP molecules (for example) is sensitive to a web of more physical factors like electromagnetic fields, ion channels, thermal fluctuations, etc. If we ignore all these contingencies, we lose causal closure again. If we include them, our mental software becomes even more complicated.

If we have to pay attention to all the contingencies of all the factors described in Cao 2022, we end up with an astronomical array of biophysical details that result in a very complex program. It may be intractable to capture all such dynamics in a simulation on Earth.

Conclusion

I think that Practical CF, the claim that we could realistically run a conscious simulation of a human brain with a classical computer on Earth, is probably wrong.

Practical CF requires the existence of a simple, causally closed and mind-explaining level of abstraction in the brain, a “software/hardware separation”. But such a notion melts under theoretical and empirical scrutiny. Evolutionary constraints and biophysical contingencies imply an entanglement between levels of abstraction in the brain, preventing any clear distinction between software and hardware.

But if we just include all the physics that could possibly be important for the mind in the simulation, would it be conscious then? I’ll try to answer this in the next post.

Appendix: Defining a simulation of a physical process

A program $P$ can be defined as^[7]: a partial function $P:{\Sigma }^{\ast }\to {\Sigma }^{\ast }$, where $\Sigma$ is a finite alphabet (the "language" in which the program is written), and ${\Sigma }^{\ast }$ represents all possible strings over this alphabet (the set of all possible inputs and outputs).

Denote a physical process that starts with initial state $s_1\in S$ and ends with final state $s_2\in S$ by $[s_1,s_2]$, where $S$ is the space of all possible physical configurations (specifying physics down to, say, the Planck length). Denote the space of possible abstractions as $A=\{a\in A|a:S\to S^{\prime }\}$ where $|S^{\prime }|<|S|$, such that $a\left(s\right)$ contains some subset of the information in $s$.

I consider a program $P$ to be running a simulation of physical process $[s_1,s_2]$ up to abstraction $a$ if $P$ outputs $a\left(s_2\right)$ when given $a\left(s_1\right)$ for all $s_1$ and $s_2$.

1. ^{^}

    1 second of simulated time is computed at least every second in base reality.

2. ^{^}

    Recall from the last post that an atom-level simulation would cost at least $2^{{10}^{26}}$ FLOPS. The theoretical maximum FLOPS of an Earth-bound classical computer is something like $2^{35}$. So the abstraction must be, in a manner of speaking, $2^{{10}^{22}}$ times simpler than the full physical description of the brain.

3. ^{^}

   If armed with a perfect understanding of how brain states correlate with experiences.

4. ^{^}

    I’m cashing in my “assuming materialism” card.

5. ^{^}

    One may argue that brains do download and run new software in the sense that we can learn new things and adapt to different environments. But this is really the same program (the mind) simply operating with different inputs, just as a web browser is the same program regardless of which website you visit.

6. ^{^}

    This analogy doesn’t capture the full picture, since programmers don’t have power over hardware. A closer parallel would be one where Alice and Bob are building the whole system from scratch including the hardware. Bob wouldn’t just entangle different levels of software abstraction, he would entangle the software and the hardware.

7. ^{^}

    Other equivalent definitions e.g. operations of a Turing machine or a sequence of Lambda expressions, are available.